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Annales Polonici Mathematici

2015 | 115 | 3 | 275-295

Higher-order linear differential equations with solutions having a prescribed sequence of zeros and lying in the Dirichlet space

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Abstrakty

EN
The aim of this paper is to consider the following three problems:i
(1) for a given uniformly q-separated sequence satisfying certain conditions, find a coefficient function A(z) analytic in the unit disc such that f''' + A(z)f = 0 possesses a solution having zeros precisely at the points of this sequence;
(2) find necessary and sufficient conditions for the differential equation
$f^{(k)} + A_{k-1}f^{(k-1)} + ⋯ + A₁f' + A₀f = 0$ (*)
in the unit disc to be Blaschke-oscillatory;
(3) find sufficient conditions on the analytic coefficients of the differential equation (*) for all analytic solutions to belong to the Dirichlet space 𝓓.
Our results are a generalization of some earlier results due to J. Heittokangas and J. Gröhn.

275-295

wydano
2015

Twórcy

autor
• Institute of Mathematics and Information, Jiangxi Normal University, Nanchang, 330022, China